I’ve been having the “Invalid Authorization” problem with the trading post from pretty much day one. If I turn off Windows firewall, the problem went away but that’s not a valid solution. I ended up having to go to the Advanced settings -> Outbound Rules and adding an “any any” outgoing rule for gw2.exe. Granted, I was lazy for not restricting the program to just what it needed but given what the other rules that were added by default, the security’s no worse that what it was.
The “Allow a program or feature through Windows Firewall” button appears to only be for incoming traffic rather than outgoing. This is what I originally chose but found gw2.exe was already there. Adding the outbound rule is what fixed the trading post.
Hopefully this will help somebody else. The OS is Windows 7 64-bit SP1 with all of the windows updates. You shouldn’t have to turn off the Windows Firewall or run GW2 in administrator mode since these really do compromise security.